What the rules say
The pet must have lived more than six months, outside quarantine, in a Group A or Group B country. Documentary evidence of that residency is required. A country on neither list is not eligible for direct entry.
Group A: Australia, American Samoa, Christmas Island, Cook Islands, Federated States of Micronesia, French Polynesia, Kingdom of Tonga, Kiribati, Marshall Islands, Nauru, New Caledonia, New Zealand, Niue, Palau, Papua New Guinea, Samoa, Solomon Islands, Tuvalu, Vanuatu, Wallis and Futuna.
Group B includes the United States (including Guam and Hawaii), Canada, the United Kingdom, and the other countries named on page 1 of the notice: Antigua and Barbuda, Aruba, Argentina, Austria, Bahamas, Bahrain, Barbados, Belgium, Bermuda, Brunei Darussalam, Bulgaria, Cayman Islands, Chile, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Falkland Islands (Malvinas), Finland, France, Germany, Gibraltar, Greece, Greenland, Guernsey, Hong Kong, Hungary, Iceland, Ireland, Isle of Man, Israel, Italy, Jamaica, Japan, Jersey, Kuwait, Latvia, Liechtenstein, Lithuania, Luxembourg, Macao, Malta, Monaco, Montenegro, Netherlands, Northern Mariana Islands, Norway, Poland, Portugal, Puerto Rico, Qatar, Reunion, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Serbia, Seychelles, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Trinidad and Tobago, United Arab Emirates, Uruguay, Virgin Islands (British), and Virgin Islands (United States of America).
The BAF pets page, written for animals being imported, says these are not allowed into Fiji: Dogo Argentine, Fila Brazileiro, Japanese Tosa, pit bull terriers including American pit bull terriers or crosses of any of these breeds, serval cats and serval crosses within five generations, cats and dogs under 4 months, and females more than 21 days pregnant. The vessel section of the September 2024 notice does not repeat that list. Check with BAF for your situation.
The vessel section is about cats and dogs. The Ships and Vessels page says other species are prohibited on yachts, and it gives separate Newcastle-disease rules for pet birds. Check with BAF for your situation.
BAF notice, 25 September 2024, page 1 and Section II.3.1 (PDF)
BAF pets page, prohibited breeds and ages
BAF Ships and Vessels, live animals on yachts